UV coordinates scale with changes in object scale?
You can try to use Vertex Slide instead of scaling.
Select the vertices / edge you want to transform and hit 2 x G or Shift+V to Vertex Slide. Move it to desired location and make sure you have Correct UVs checked in the options (left T panel).
You can use keyboard to set the exact value while sliding (I set -3 in the video).

If you need to extend the vertices outside, start sliding and keep Alt pressed.